On harmonic and biharmonic Bézier surfaces

Authors:
J. Monterde;H. Ugail
Affiliations:
Departamento de Geometria i Topologia, Universitat de València, Avd. Vicent Andrés Estellés, 1, E-46100-Burjassot, València, Spain;Department of Electronic Imaging and Media Communications, School of Informatics, University of Bradford, Bradford BD7 1DP, United Kingdom
Venue:
Computer Aided Geometric Design
Year:
2004

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Abstract

We present a new method of surface generation from prescribed boundaries based on the elliptic partial differential operators. In particular, we focus on the study of the so-called harmonic and biharmonic Bézier surfaces. The main result we report here is that any biharmonic Bézier surface is fully determined by the boundary control points. We compare the new method, by way of practical examples, with some related methods such as surfaces generation using discretisation masks and functional minimisations.